Finite Group Databasebeta

D47×#2177 #26369577

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2177

Splittings

FittingC47×#2177 ⋊ C2
SylowC47 ⋊ C2×#2177

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2177C2
socleC22×C47C22×D8
prime radicalC2×D16×D47C2
cosocleC2×C8×C47C24
hypercenter#2177D47
hypocenterC47C2×#2177
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

798 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322867);